Dynamic Touch: Muscles as the Medium
Week 4: Dynamics of Perception & Action
Recap: Action-Scaled World
We have seen that we perceive the world in terms of our capabilities.
- Optic Flow: Where am I going? (Locomotion)
- Affordances: What can I do? (Climbing, Passing through)
- Body Scaling: How do I fit? (() numbers)
Today: How do we perceive the world through our body?
The Problem: The Blind Man’s Cane
“If a blind man uses a cane, he feels the sidewalk, not the cane.” — Merleau-Ponty / Gibson
- Proximal Stimulus: Pressure on the palm of the hand.
- Distal Perception: The texture and distance of the sidewalk.
How do we perceive the tip of the tool when we are holding the handle?
Three Kinds of Touch
- Cutaneous Touch: (Passive)
- Stimulation of skin (heat, texture, pain).
- Example: A fly landing on your arm.
- Haptic Touch: (Active)
- Exploratory movement of hands.
- Example: Identifying a key in your pocket.
- Dynamic Touch: (Effortful)
- Muscular exertion / Wielding.
- Example: Swinging a tennis racket.
The Wielding Experiment
Solomon & Turvey (1988)
- Task: Hold a rod behind a curtain. Wield it (wrist only).
- Question: How long is it?
- Result: Participants are incredibly accurate ((r^2 = .99)).
Crucial Point: They never see the rod. They never touch the tip. They only feel the forces in the handle.
Hypothesis 1: Is it Mass (Weight)?
If I give you a heavy rod and a light rod, does the heavy one feel longer?
- Not necessarily.
- A short, heavy steel rod feels short and heavy.
- A long, light wooden rod feels long and light.
Conclusion: Mass alone does not specify length.
The Physics of Rotation
When you wield an object, you are rotating it. To rotate an object, you must overcome its resistance to rotation.
Moment of Inertia ((I)): \[ I = m \times d^2 \]
- (m) = Mass (How heavy is it?)
- (d) = Distance of mass from axis of rotation (How far away is it?)
Why Distance Matters
Imagine holding a sledgehammer.
- Hold the handle: Heavy head is far away ((d) is large). Hard to rotate. Feels Long.
- Hold the head: Heavy head is close ((d) is small). Easy to rotate. Feels Short.
The Moment of Inertia specifies the reachability of the object.
The Inertia Tensor ((I_{ij}))
Objects aren’t just lines. They are 3D shapes. You can rotate them in 3 dimensions (Pitch, Yaw, Roll).
The Inertia Tensor is a (3 ) matrix that captures resistance to rotation in all directions.
\[ I = \begin{bmatrix}
I_{xx} & I_{xy} & I_{xz} \\
I_{yx} & I_{yy} & I_{yz} \\
I_{zx} & I_{zy} & I_{zz}
\end{bmatrix} \]
Perception via Dynamics
| Moment of Inertia ((I)) |
\(\rightarrow\) |
| Product of Inertia ((I_{xy})) |
\(\rightarrow\) |
| Principal Axes |
\(\rightarrow\) |
We detect the invariant physical dynamics (Inertia) to perceive the variant spatial properties (Length).
Next Class: Thursday
Activity: “The Wielding Game”
- You will wield unseen objects.
- You will predict their length and shape.
- We will see if you are sensitive to the Inertia Tensor.
Reading: * Turvey & Carello (1995) * Blau & Wagman Chapter 8